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Of course it does. It's called the infinitesimal. It's common definition for real number is 1 / infinity: https://en.wikipedia.org/wiki/Infinitesimal https://en

Of course it does. It's called the infinitesimal. It's common definition for real number is 1 / infinity: https://en.wikipedia.org/wiki/Infinitesimal https://en.wikipedia.org/wiki/Infinitesimal If you've taken Calculus, you've already worked with math that requires the infinitesimal to exist. It's not a value you can meaningfully write out, but you can't write out pi, e, phi, root 2, 1 / 3 in base 10, root -1, etc. "I can't write it down" isn't a particularly unique property for numbers.

pwdisswordfish2 7y ago
There is no smallest positive infinitesimal either. At least in theories that manage to define those rigorously. And it’s mostly a formal trick anyway; standard epsilon-delta calculus avoids them entirely. Had you actually meaningfully studied this subject, or did you just link to a Wikipedia article you half-heartedly skimmed one day?
- da_chicken 7y ago
  That's a funny way to say, "No, I think you misunderstand. I mean to say no single infinitesimal number exists. Like infinity, the concept exists, but as a literal single number, no."
- camelite 7y ago
  > There is no smallest positive infinitesimal either. There is in the surreal and hyperreal number systems. I got that from skimming wikipedia though....
gspr 7y ago
> If you've taken Calculus, you've already worked with math that requires the infinitesimal to exist. Not at all. Standard calculus uses standard real numbers, for which there is no infinitesimal. One may well speak of infinitesimals as a mental tool when building a mental model for calculus, but those infinitesimals are not actual real numbers (or a well-defined mathematical object at all - in standard calculus).
- brlewis 7y ago
  Correct. This is covered in the article. https://en.wikipedia.org/wiki/0.999...#Infinitesimals https://en.wikipedia.org/wiki/0.999...#Infinitesimals
petters 7y ago
At the very least, don't write "Of course it does". It does not in the real number system.
deleted 7y ago
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pwdisswordfish2 7y ago

There is no smallest positive infinitesimal either. At least in theories that manage to define those rigorously. And it’s mostly a formal trick anyway; standard epsilon-delta calculus avoids them entirely. Had you actually meaningfully studied this subject, or did you just link to a Wikipedia article you half-heartedly skimmed one day?

da_chicken 7y ago
That's a funny way to say, "No, I think you misunderstand. I mean to say no single infinitesimal number exists. Like infinity, the concept exists, but as a literal single number, no."
camelite 7y ago
> There is no smallest positive infinitesimal either. There is in the surreal and hyperreal number systems. I got that from skimming wikipedia though....

gspr 7y ago

> If you've taken Calculus, you've already worked with math that requires the infinitesimal to exist. Not at all. Standard calculus uses standard real numbers, for which there is no infinitesimal. One may well speak of infinitesimals as a mental tool when building a mental model for calculus, but those infinitesimals are not actual real numbers (or a well-defined mathematical object at all - in standard calculus).

brlewis 7y ago
Correct. This is covered in the article. https://en.wikipedia.org/wiki/0.999...#Infinitesimals https://en.wikipedia.org/wiki/0.999...#Infinitesimals

petters 7y ago

At the very least, don't write "Of course it does". It does not in the real number system.

deleted 7y ago

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